1. Field of the Invention
The present invention relates to the design of interferometers, and more specifically, it relates to the design of single interferometers and pairs of interferometers which can use broadband uncollimated light from an extended source.
2. Description of Related Art
Interferometers in single and in double arrangements are very useful devices in a variety of applications in optics, metrology and communications. These interferometers have a delay .tau. between their arms which can produce fringes in the output density. Single interferometers having zero or near zero delay can be used with short coherence illumination to compare distances between one arm containing a sample and a reference arm. Single interferometers having larger delays can be used to measure the spectrum of a source, or to measure Doppler shifts of laser illuminated targets to measure motion, since slight differences in wavelength (.lambda.) cause changes in fringe phase. Double interferometers having non-zero delays are useful in optical communications and measurement of velocity of targets illuminated by broadband radiation.
Prior art interferometers have a design which requires parallel light, or which is not optimized for very broadband usage, or was impractical for very long delays. Consequently, these interferometers are impractical for many applications involving white light and light from an extended source, such as from a common lamp, which produces non-parallel (uncollimated) beams. This is a serious handicap, because the majority of inexpensive compact sources are then excluded.
The present invention includes the use of interferometers, in single or in pairs, which are capable of working with broadband uncollimated light. These are called achromatic "superimposing" interferometers because they superimpose the images or ray paths associated with each interferometer arm. A similar concept has been discussed previously by others and called "field compensation." However, previous interferometer designs may have been superimposing only for a very limited wavelength range, or are impractical to create large delays, or are impractical to scan the delay.
Generally, the goal in a superimposing interferometer is to split an input beam into two or more separate beams, coherently delay one beam relative to the other, and recombined them to form an output beam. (Usually just two beams are split and recombined in the case of a Michelson-type interferometer, or an infinite number in the case of a recirculating Fabry-Perot type interferometer). The separate, splitted beams are also called interferometer "arms", and the arms can have different lengths which create a relative delay. For each input pulse, two or more pulses are outputted. The earliest output pulse, from the shortest arm, could be called the "undelayed" signal. The later pulses, from the longer arms, are called "echos." The interval between the undelayed signal and the echo is the interferometer delay .tau..
The term "coherently delayed" is explained in FIG. 1A. A pattern of light (which could be called an image) may be presented to the input image plane 40, and the interferometer transports the pattern to an output plane 42 by imaging optics, so that there is a correspondence between input and output pixels 46 and 50, and between 44 and 48. The pattern appears for each instance of the output pulses discussed above. We are interested in the delay between instances. The term "coherently" delayed means that the time delay .tau..sub.1 for rays of light arriving at output pixel 50 is the same for all the rays of the bundle arriving at 50, within a tolerance of a quarter wave (a time interval of .lambda./4c, where c is the speed of the wave). The delay associated with another output pixel 48 could be called .tau..sub.2, and this may be different or the same at .tau..sub.1. Thus, even though the delay .tau. may change from output pixel to pixel, within the bundle of rays associated with each pixel the delay is very uniform. This uniformity is necessary to create fringes having significant contrast (visibility).
In some applications it is desired that .tau. have the same value for all pixels of the input beam. This will produce an infinitely wide fringe on output of the interferometer. In other applications it may be desired that .tau. vary linearly across the output beam. This will generate an evenly spaced and parallel fringe "comb", where the phrase of the fringe varies linearly transversely across the beam. (This is usually easily accomplished by tilting an interferometer arm end mirror). Only superimposing interferometers can produce infinitely wide or evenly spaced parallel fringe combs. (Conventional Michelson interferometers produce rings of fringes which are not linear of evenly spaced, except very far off axis). A superimposing interferometer could also be called angle-independent or solid-angle independent, because .tau. is independent of the angle of each ray within the bundle associated with a given image pixel.
A note on terminology: the delay value can be specified several ways, by single-trip path length D, by the round trip path length c.tau., or by a time interval .tau.. Strictly speaking, the units of .tau. should be time, but for convenience .tau. is sometimes specified in terms of length units, in which case it is implied that the length should be first divided by c to yield the equivalent time value. Secondly, these delay values usually refer to the difference in path length or travel times between interferometer arms, except when an isolated means for creating a delay is discussed, in which case it could refer to the propagation time through this means. When an optical element or assembly is inserted into an optical path, the increase in the propagation time t causes over the original time is called an "insertion" delay. For example, a 20 mm thick glass etalon having a refractive index of n=1.5 would have an insertion delay .DELTA.D=(n-1)20=10 mm, due to the slower propagation of light through glass compared to vacuum or air. Thirdly, the term "delay" has dual meanings in this document. It may refer to a value, such as .tau., c.tau. or D, or it may refer to the means for creating the delay value, such as "an etalon delay" or a "relay delay".
FIG. 2A shows a common Michelson consisting of a beamsplitter 24 and two end mirrors 20 and 22. This interferometer is not superimposing because mirrors 20 and 22 do not superimpose in view of the beamsplitter. This has the consequence that .tau. has depends on incident ray angle. The single-trip path lengths between the beamsplitter and end mirrors differ by an amount D for rays parallel to the optic axis. This causes a round trip delay time of .tau.=2D/c between the two arms, where c is the speed of the illumination (which is spoken of as light, but can be any radiation that travels as rays, such as microwaves, sound, x-rays). FIG. 2B shows the optical equivalent of FIG. 2A, because the partial reflection off the beamsplitting surface 24 puts the two mirrors 20 and 22 apparently in the same path, but longitudinally displaced. When a ray of light 25 enters with an angle .theta. to the optic axis, it encounters a path difference which depends on angle as 2Dcos.theta.. Thus the delay deviates from its nominal value of .tau. by .tau.(1-cos.theta.), which is of the order (1/2).tau..theta..sup.2, for small angles with .theta. in radians. This deviation can smear the delay which reduces fringe visibility. Note also that the ray 10 reflecting off mirror 20 does not overlap the path of ray 11 from the other mirror 22. For the same reason, an object seen in reflection of the two mirrors 20 and 22 will be seen as two images that are longitudinally displaced. Thus, the Michelson having a nonzero delay does not superimpose ray paths nor images, except for perfectly parallel incident light. The non-superposition and the angle-dependence of the interferometer are related.
The common Fabry-Perot interferometer (FIG. 2C) consisting of two flat partially reflecting mirrors 21, 23 separated by a distance D, is non-superimposing and suffers an angle dependence to the delay analogous to the Michelson example. The output rays 26, 27, 28 for a single given input ray 29 do not superimpose in path. Furthermore, the multiple images of an object observed through the interferometer will be longitudinally displaced from each other. Thus this interferometer does not superimpose paths nor images.
The angle dependence of these non-superimposing interferometers creates practical difficulties, because the fringe visibility is small unless the incident light is very parallel. An illumination source producing rays having a range of cone angles up to .theta. will smear the delay by .about.(1/2).tau..theta..sup.2, which destroys the fringe visibility if this is more than a quarter wave (.lambda./c4). This puts a limit of .theta..about.(.lambda./2c.tau.).sup.1/2 for the maximum cone angle. In order to produce this degree of parallelism from an ordinary lamp, which is an extended source, a small pinhole must be used a far distance from the interferometer. This greatly reduces the amount of power available from the lamp. For example, for a 4-meter delay (such as used to measure Doppler velocities typical of automobiles) and green light (.lambda.=500 nm), .theta. must be less than 0.00025 radian. This limits the numerical aperture of the illumination source to f/2000, which greatly reduces the amount of power available from a filament. Secondly, this restriction on parallelism also applies to the reflected light from the target as it enters the detecting interferometer in a velocity interferometer application. This severely reduces the depth of field of the target motion, so that when the optics imaging the target into the interferometer become slightly out of focus, visibility of the fringes is diminished.
Single interferometers (Fabry-Perot and Michelson) are used as for spectroscopy, such as Fourier Transform spectroscopy. The small cone-angle tolerance of these non-superimposing interferometers limits the spectral resolution. A book by R. Beer shows that for conventional Michelson interferometers there is a reciprocal relationship between the solid angle .OMEGA.=.pi..theta..sup.2 of a source and the best resolution (.lambda./.DELTA..lambda.) achieved with a single channel detector, so the higher the spectral resolution the smaller the signal power. (Reinhard Beer, "Remote Sensing by Fourier Transform Spectrometry", John Wiley & sons, NY 1992, QD96.F68B43, page 17). The limit on .OMEGA. for a given spectral resolution severely limits the etendue or light gathering power (beam area times .OMEGA.), and prevents high spectral resolution on diffuse sources such as the aurora, plasmas, light from speckling images of stars, or light communicated through large diameter optical fibers.
In contrast, with a superimposing interferometer the delay is independent of ray angle and all the light can be accepted from an extended source and have the same delay imprinted on it coherently. This can dramatically increase signal power. For the above example where the numerical aperture of a conventional Michelson was limited to f/2000, for a superimposing Michelson the numerical aperture could be, say f/10. It is not limited by anything having to do with the delay time, but instead by the diameter of the optics used in its construction. The amount of light power is increased by the ratio (2000/10).sup.2 or 40,000. This is a tremendous advantage.
A method of making an angle-independent delay is to superimpose the ray paths (FIG. 1B) associated with each interferometer arm. This is the best solution. A less desirable method, but still useful, is to superimpose images associated with each interferometer arm (FIG. 1C). FIG. 1B shows the rays for a single pulse 58 that enters a pixel at the input image plane will appear at a pixel at the output plane, and there will be at least one echo 56 to the main signal 60, and that the ray paths for the echos superimpose the paths of the main signal. In FIG. 1C the rays for the echos 52 and signal 54 do not share the same path, but still intersect at the output pixel. Note that superimposing paths automatically superimposes images, but not vice versa. Superimposing paths is preferred because then the detector can be placed anywhere along the output optical path. If only images are superimposed, then the detector must be placed at the output plane or a re-image of this plane, otherwise the rays from all the arms do not intersect properly at the appropriate pixels and the fringe visibility is poor. Devices that are ideally designed to superimpose paths may in practice have slight aberrations that cause the paths of one arm to deviate from the intended path, so that strictly speaking only a superimposition of images is achieved. Thus there is not a black-and-white distinction between the two kinds, it is a matter of degree.
FIG. 1D shows an example, using a Michelson interferometer having zero delay. The interferometer has a plane mirror 62, and an irregular mirror 64 superimposed longitudinally in reflection of the beamsplitting surface 68. Let both the input and output planes 65 be at these mirrors. Then the irregular surface of mirror 64 will cause the output ray 67 to have a different angle and hence path than output ray 66 from the flat mirror, yet both rays appear to come from the same pixel 69 of the output plane. Thus images are superimposed while paths are not. In these cases, it is very important that the detector be at the output image plane or a re-image of that plane. This discussion is meant to illustrate the utility of defining input and output planes for realistic interferometers, that is, those having slight aberrations.
The ray path superposition principle has been discussed in the design of the spherical Fabry-Perot (FIG. 3A) [Pierre Connes, "L'Etalon de Fabry-Perot Spherique", Le Journal De Physique et le Radium 19, p262-269 (1958)], and the wide-angle Michelson interferometer [R. L. Hilliard and G. G. Shepherd, "Wide-angle Michelson Interferometer for Measuring Doppler Line Widths", J. Opt. Soc. Am. 56, p362-369 (1965)], where it was called "field compensation". These interferometer designs have properties that discourage or prevent their use in applications where broadband illumination is used, or long delays are needed, or adjustability of delay is desired.
FIG. 3A shows a Spherical Fabry-Perot, consisting of two spherical mirrors spaced such that the two mirror focal points 30 coincide in the middle of the distance separating the mirrors. Each mirror has a half 32 which is totally reflective, and a half 33 which is partially reflective. A ray 34 entering the cavity recirculates between the left and right mirrors, emitting a series of output pulses with geometrically decreasing intensities. The interval between output pulses is called the interferometer delay .tau.. Because of the overlap of foci, .tau. is independent of input ray path and the output rays for a given input ray 34 superimpose in output path 35.
The bottom half 32 of each mirror must be totally reflecting to allow only rays that have made an even number of round trips between the left/right halves to emerge. If both halves (32, 33) of the mirror were partially transparent, then output rays would be emitted which would not superimpose with rays 35. Another way to think about it is that if both halves were partially transparent, then an image plus an upside down version of that image would be outputted. The presence of the upside image would spoil the fringe visibility. Note that the edge between the totally 32 and partially reflective halves 33 lies on the optic axis 31. This is inconvenient because it prevents full use of the circular region of the output image around the optic axis where aberrations, such as spherical aberration, are smallest. The spherical Fabry-Perot must therefore be used slightly off-axis.
For the Spherical Fabry-Perot it is not possible to adjust .tau. and maintain the superimposing condition because the focal lengths are fixed. FIG. 3B shows that when the separation of the mirrors is changed, the two mirror foci 36 come out of overlap. Then the undelayed 37 and first echo output ray 38 for a given input ray no longer superimpose and the delay .tau. becomes dependent on input ray path.
The wide-angle Michelson discussed by R. L. Hilliard achieves path superposition for monochromatic light by use of a glass etalon, as shown in FIG. 4A. Due to refraction through the glass etalon 76, the mirror 72 behind the etalon appears at 74, close to the beamsplitter 71 by a displacement B given by T(n-1)/n, where T is the etalon thickness and n is the refractive index of the etalon. Mirror 70 of the other arm is arranged to superimpose with the apparent mirror position 74. This creates a time delay between the two arms due to the sum of two effects: the actual mirrors are at different distances from the beamsplitter, and secondly, light travels slower through glass by the factor n. The net delay is c.tau.=2[T(n-1)/n+T(n-1)].
Due to glass dispersion the apparent mirror position 74 is different for different wavelengths. This prevents the superposition condition to be achieved for all the wavelengths of white light, so that this interferometer is inappropriate for a white light velocity interferometer. Secondly, long delays such as c.tau.=4 meters, are not practical. (These long delays are useful for measuring meter/sec velocities found in industry). Thirdly, the delay value cannot be adjusted by a significant amount. (Tilting the etalon adjusts it slightly, but introduces astigmatism).
These disadvantages are not important when the etalon Michelson (FIG. 4A) is used as a velocity interferometer with monochromatic laser illumination. However, there is great utility in being able to use cheap ordinary white light sources for illumination instead of an expensive laser, and these call for a different kind of interferometer.
Recently, an interferometric method of using broadband illumination to measure target motion has been invented by the present author. The theory of operation is described in U.S. Pat. No. 5,642,194 by David J. Erskine, which is included herein by reference. In concept, it uses two interferometers in series, with the target interposed. In order to use white light, and uncollimated light from extended sources, the interferometers must be superimposing for a wide range of wavelengths. Furthermore, in order to measure slow velocities, of order meter/second, long delays of several meters in length are needed. In this white light velocity interferometer, the two interferometer delays must match. This requires adjustability of the second interferometer delay. All these requirements hinder practical use of the prior art interferometers in the white light interferometer, or in other double interferometer applications, such as communication, where incoherent lamps or multimode fibers are desired for illumination sources.
The topology of a double superimposing interferometer configuration used for broadband velocimetry is shown in FIG. 5A. (The configuration for optical communication is similar, except the target 5 is omitted). Two superimposing interferometers (3 & 7) are in series with an interposed target 5 and illuminated by a broadband source 1. When the delays .tau..sub.1 and .tau..sub.2 match within a coherence length of the source illumination, fringes are created in the intensity of the outputs 8, 9, which are complementary in phase. In some embodiments, a single actual interferometer is used to implement the first and second conceptual interferometers by using retro-reflected light from the target. This automatically matches .tau..sub.1 =.tau..sub.2, in spite of gross mechanical vibration of the instrument that may change .tau.. This makes the retro-reflecting configuration attractive for industrial environments, and reduces weight and cost of the optical platform, since this does not have to be as rigid.
Target displacement or refractive index along the round trip path to the target during the interval .tau. cause a proportional shift .DELTA..phi. in the fringe phase, where .phi. is in units of fringe. (One fringe is 1 revolution, 360.degree. or 2.pi. radians). Thus, this is essentially a radial velocity measurement, as opposed to some other systems which measure transverse velocity (such as those involving the intersection of two incident laser beams to create standing waves, through which a particle to be measured travels). However, the combination of several simultaneous radial velocity measurements taken at different angles to the target can provide all 3 components of the velocity vector if desired.
When the light reflects normally off the target so that it approximately doubles back on itself, the displacement .DELTA.x during an interval .tau. is EQU .DELTA.x=(.lambda./2).DELTA..phi.
and the average velocity v over that interval is EQU v=(.lambda./2.tau.).DELTA..phi.
so that the velocity per fringe proportionality is (.lambda./2.tau.). The phase shift produced by a moving target is .DELTA..phi.=v (2.tau./.lambda.). Hence, in order to produce a significant fringe shift to detect a slow moving target, long delays are desired. A c.tau.=4 meter delay produces a fringe shift porportionality of .about.20 m/s per fringe. Since fractional fringe shifts down to .lambda./100 can be easily measured, a 4-meter delay can have a velocity resolution of 0.2 m/s, suitable for industrial settings. Now the challenge is to build a 4-meter superimposing interferometer that is achromatic. Clearly, a 4-meter thick glass etalon is not practical due to its cost and chromatic aberration. Some of the designs presented below are a solution to this challenge.
There are different ways of detecting and interpreting the interferometer output. The output light can be detected by a single detector that is sensitive to a wide bandwidth, in which case an average .lambda. is used. Alternatively, the output can be spectrally resolved into multiple channels. In this case, the velocity can be computed for each channel using the .lambda. specific to each channel. These will give redundant velocity answers which can be used to check for consistency.
One advantage of using wide bandwidth illumination is the unambiguous velocity determination. That is, the lack of integer fringe skips when the velocity jumps more rapidly than the detecting electronics can follow. Essentially, the velocity measurement taken in different colors, such as red, green, blue, can be combined to determine the absolute velocity unambiguously, even though individually each color channel may have an integer fringe ambiguity. This is because each channel has a different velocity per fringe proportionality.
In contrast, in the conventional monochromatically illuminated systems, the fringe phase is ambiguous to an integer due to the periodicity of monochromatic fringes. This creates a great uncertainty in the gross value of the velocity when the target is first acquired (such as a car coming over the horizon) or if the signal drops out temporarily. This fringe skip uncertainty hinders the use of these monochromatic systems in applications where there is no other confirming method of velocity measurement, or where theoretical prediction of velocity is poor.
A similar velocimetry method using two Fabry-Perot interferometers and laser illumination was described in a journal article by S. Gidot and G. Behar, "Multiple-line laser Doppler velocimetry", Appl. Opt. 27, p2316-2319 (1988). However, since the Fabry-Perot is not a superimposing interferometer, this method is not practical with uncollimated illumination. Uncollimated rays passing through the Fabry-Perot will blur the delay value, which can cause a loss of fringe visibility. This produces a severe trade-off between degree of non-parallelism and maximum source bandwidth which preclude practical use of common white light sources such as lamps.
FIG. 4B shows what is meant by the term "beam shortening", which is an important part of creating a superimposing interferometer. When real or virtual imaging by an optical element 966 causes an object or source 960 to appear by ray tracing to be at a different location 962 than the actual physical location 960, then the difference 964 is called a beam shortening or beam length shortening. The beam length could be measured from some reference plane 968. The apparent beam length 970 is from plane 968 to the apparent object location 962. The physical beam length 972 is from plane 968 to the physical object location 960. FIG. 4B shows a positive beam shortening, when the apparent beam length is less than the physical beam length. Negative beam shortenings are also possible.
In those interferometers where the beam reflects off an end mirror, such as 72 in FIG. 4A, and nearly doubles back on itself, the beam shortening changes the position of the end mirror 72 from its physical position 72 to an apparent position 74. The roundtrip beam shortening would be twice B. When beam shortening involves an end mirror, the combination of the end mirror and the optical element performing the imaging could be called a "delaying mirror". In FIG. 4A, the delaying mirror would be etalon 76 and end mirror 72. The term "delaying mirror" replaces the term "superimposing delay" used in the previously mentioned U.S. Pat. No. 5,642,94 by the present author.
A delaying mirror is a set of optics that acts like a mirror in terms of ray tracing, but delays the waves in time compared to an actual mirror. Delaying mirrors are useful elements in forming a superimposing interferometer. This document present designs of delaying mirrors and designs of superimposing interferometers that may be useful because of their achromatic character, their possible long delay times, adjustability, or wide image field.